Simplify the following expression: $ t = -1 + \dfrac{9}{-7r + 2} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-7r + 2}{-7r + 2}$ $ \dfrac{-1}{1} \times \dfrac{-7r + 2}{-7r + 2} = \dfrac{7r - 2}{-7r + 2} $ Therefore $ t = \dfrac{7r - 2}{-7r + 2} + \dfrac{9}{-7r + 2} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{7r - 2 + 9}{-7r + 2} $ $t = \dfrac{7r + 7}{-7r + 2}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{-7r - 7}{7r - 2}$